Finite Group Databasebeta

C2×#20246111 #26375079

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×#20246111

Splittings

FittingC2×C47×#382 ⋊ C2
SylowC47 ⋊ C2×#2328

Subgroups

subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#382C2
socleC24×C47C24
prime radicalC22×#13094021C2
cosocleC23×C47C25
hypercenterC2×#382D47
hypocenterC47C2×#2328
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#382

4430 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 328369);